How to Quickly Calculate Square of Any Two Digit Number?

In this post I’ve tried to improvise on the method of squaring presented in one of the earlier posts on Quickermaths.com itself. This trick of squaring any two digit number with ease is inspired by squaring techniques from the book – The Trachtenberg Speed System of Basic Mathematics

I would like to explain this method of squaring any 2 digits number with the help of an illustration.

What is the square of 32?

Step 1. In finding the last two digits of the answer, we shall find the square of the last digit of the number. Square the right-digit digit, which is 2 in this case. Hence we get 04

_ _04

Step 2. We shall now need to use the cross product. This is what we get when we multiply the two digits of the given number together. Multiply the two digits of the number together and double it: 3 times 2 is 6, doubled is 12: We write 12 as 2 and carry over 1 to the next step.

_ 24

Step 3: In finding the first two digits of the answer we shall still need to square the first digit of the number. That means we square the left hand figure of the number. Here square of 3 will be 9. Add 1 which is carried over from last step. Hence we get 9 + 1 =10

1024

That’s the answer.

This method can also be compared with another shortcut to find the square of any number posted by me on Quickermaths.com in the past.

Let’s try another example by squaring 64.

Square of 64 =     Square of 6 | double of cross product of both given digits 4 & 6| square of 4

Square of 64 =      36 |2x6x4 | 16

=      36 | 48 | 16

Collapsing the numbers

=      36 | 48 + 1 | 6

=      36 + 4 | 9 | 6

=      40 | 9 | 6

Hence the answer is 4096.

Have you come across any other squaring method like this?

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